Re-derive the incompressibility condition: starting from $\partial\rho…

Question

Re-derive the incompressibility condition: starting from $\partialho/\partial t + 
abla\cdot(ho\mathbf{u}) = 0$ with ρ = const, what remains?

Accepted Answer

B. {'text': '$\nabla\cdot\mathbf{u} = 0$', 'label': 'B'}

With ρ = const: ∂ρ/∂t = 0 and ρ factors out of divergence. We get ρ∇·u = 0, so ∇·u = 0. Incompressible flow has zero velocity divergence.

Answer

{'text': '$\rho = \nabla\cdot\mathbf{u}$', 'label': 'A'}

Answer

{'text': '$\partial\rho/\partial t = 0$ only', 'label': 'C'}

Answer

{'text': '$\rho\mathbf{u} = 0$', 'label': 'D'}

Re-derive the incompressibility condition: starting from $\partial\rho/\partial t + \nabla\cdot(\rho\mathbf{u}) = 0$ with ρ = const, what remains?